1. The problem asks for the equation of a line parallel to the line given by $$y = 2x + 5$$ and passing through the point $$(1,0)$$. 2. Recall that parallel lines have the same slope. The slope of the given line is the coefficient of $x$, which is $$2$$. 3. The general form of a line is $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. 4. Since the new line is parallel, it has slope $$m = 2$$. We need to find $$b$$ such that the line passes through $$(1,0)$$. 5. Substitute $$x=1$$ and $$y=0$$ into $$y = 2x + b$$: $$0 = 2(1) + b$$ 6. Simplify: $$0 = 2 + b$$ 7. Solve for $$b$$: $$b = -2$$ 8. Therefore, the equation of the line parallel to $$y = 2x + 5$$ and passing through $$(1,0)$$ is: $$y = 2x - 2$$